\section{Conclusions and Future Work}

\label{sec:conclusion}

Our implementation of PQP algorithm on a GPU is faster than the state of the art
quadratic program solvers on an average. The decrease in computation time allows
model predictive control to be applied to fast dynamics system which require
high sampling rates (where $\Delta t$ is small).

We took advantage of the sparse structure of $\lambda$; however we leave
optimization involving the use of sparse structure of $Q$ as future work, as the
sparsity of $Q$ increases significantly for larger values of $n$. For the
current problem, $r=0$ was used which resulted in reasonable convergence.
However, finding the best value for $r$ for a given problem is needs to be done.
Also, in order to use our work as a replacement for the generalized solvers, we
need more test cases from other controls applications.


